-
Summary
The main objective of this experiment was to verify the
Richardson-Zaki equation for
liquid-solid fluidization beds and to study the flow pattern and
calculate the pressure drop
characteristics of gas-solid fluidization beds. Water-sand
system was used for liquid-solid
fluidization & air-resin system was used for gas-solid
fluidization. For liquid-solid system, bed
height and superficial velocities were determined. Logarithmic
plot of superficial velocity vs.
voidage were plotted for both increasing and decreasing
velocities. From the plot values of
terminal settling velocity, minimum fluidization velocity and
Richardson-Zaki index were
determined for both increasing and decreasing velocities. The
values of ut, umf and n varied
from 0.192-0.2354m/s, 0.01547-0.01844 m/s and 2.7007-3.1382
respectively. Corresponding
theoretical values were also obtained from the (R/u2) (ud/) 2
vs. Re plot. The values of
ut, umf and n were 0.186 m/s, 0.019m/s and 2.628 respectively.
For gas-solid fluidized bed,
pressure drops for corresponding superficial velocities of air
were recorded and the graphical
relation between pressure drop and superficial air velocity were
showed in plot. The flow
regimes for different flow rates in gas-solid fluidization bed
were shown in neat sketches.
-
Experimental Setup
The following diagrams show the experimental setup for this
experiment.
Figure 1: Schematic diagram for a liquid-solid fluidization
bed.
-
Figure 2: Schematic diagram for 2-D and 3-D gas-solid
fluidization beds.
-
Flow Regimes:
Figure 3: Flow regimes for 2-D gas-solid fluidization bed.
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Observed Data
Fixed bed height = 1.2 inch
Weight of sample sand = 280g
Inner diameter of gas-solid tube = 6 inch
Initial height of bed without fixed bed height = 3 inch
Mesh Number of sand = -12+14
Room temperature = 26C
Column diameter of liquid-solid tube = 2 inch
Table 1: Observed Data for liquid-solid fluidization
No.
Of
Obs.
Increasing Flow Rate Decreasing Flow Rate
Mass of
Water
+
Bucket
(Kg)
Time
(s)
Height of the
bed
(inch)
Mass of
Water +
Bucket
(Kg)
Time
(s)
Height of
the bed
(inch)
1 0.85 30.6 3.85 5.2 30.6 8.85
2 1.05 30.5 3.8 5.05 30 8.7
3 1.125 30.25 3.875 5 30.1 8.35
4 1.3 30.5 3.975 4.6 30 7.85
5 1.35 30.5 4 3.55 30.1 6.3
6 1.5 30.2 4.2 2.4 30 5.05
7 1.62 30.5 4.35 1.9 30 4.6
8 2.3 30.5 4.8 1.55 30 4.15
9 3.45 30.8 6.2 - - -
10 4.12 30.7 7.15 - - -
11 4.8 31 8.4 - - -
12 5.2 30.5 9.1 - - -
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Table 2: Observed Data for gas-solid fluidization
No.
Of
Obs.
Flow rate
Of air
(L/min)
Height of the manometric
fluid (CCl4)
Left
(inch)
Right
(inch)
1 80 21.1 19.95
2 120 21.2 19.95
3 160 21.2 19.8
4 200 21.2 19.75
5 240 21.3 19.7
6 280 21.35 19.7
7 320 21.4 19.65
8 360 21.5 19.6
9 400 21.55 19.5
10 440 21.6 19.4
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Calculated Data
Table 3: Calculated data for flow rate, velocity and voidage for
liquid-solid fluidization bed.
Obs.
No.
Height of
fluidization
bed
(m)
Mass flow
rate
(Kg/s)
Volumetric
flow rate
(m3/s)105
Superficial
Velocity
(m/s)
Voidage
For Increasing Flow Rate
1 0.09779 0.017973856 1.80318E-05 0.008896681 0.367273
2 0.09652 0.024590164 2.46694E-05 0.012171614 0.358947
3 0.098425 0.027272727 2.73606E-05 0.013499426 0.371355
4 0.100965 0.032786885 3.28926E-05 0.016228818 0.38717
5 0.10160 0.03442623 3.45372E-05 0.017040259 0.3910
6 0.10668 0.039735099 3.98632E-05 0.019668038 0.4200
7 0.11049 0.043278689 4.34182E-05 0.02142204 0.4400
8 0.12192 0.06557377 6.57851E-05 0.032457637 0.4925
9 0.15748 0.102272727 0.000102602 0.050622848 0.607097
10 0.18161 0.124429967 0.000124831 0.061590216 0.659301
11 0.21336 0.14516129 0.000145629 0.071851785 0.7100
12 0.23114 0.160655738 0.000161174 0.07952121 0.732308
For Decreasing Flow Rate
13 0.22479 0.160130719 0.000160647 0.079261337 0.724746
14 0.22098 0.158333333 0.000158844 0.078371669 0.7200
15 0.21209 0.156146179 0.000156649 0.077289074 0.708263
16 0.19939 0.143333333 0.000143795 0.070946984 0.689682
17 0.16002 0.107973422 0.000108321 0.053444572 0.613333
18 0.12827 0.07000000 7.02256E-05 0.034648527 0.517624
19 0.11684 0.053333333 5.35052E-05 0.026398878 0.470435
20 0.10541 0.041666667 4.1801E-05 0.020624123 0.413012
21 0.1016 0.026578073 2.66637E-05 0.013155587 0.3910
22 0.10033 0.013266998 1.33098E-05 0.006566885 0.383291
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Table 4: Data for pressure drop and superficial air velocity for
Gas-Solid fluidization bed.
Obs.
No.
Pressure
Drop
(m)
Flow rate of
Air
(m3/s)103
Superficial
Air Velocity
(m/s)
1 0.02921 0.00133 0.0730994
2 0.03175 0.00200 0.1096491
3 0.03556 0.00267 0.1461988
4 0.03683 0.00333 0.1827485
5 0.04064 0.00400 0.2192982
6 0.04191 0.00467 0.255848
7 0.04445 0.00533 0.2923977
8 0.04826 0.00600 0.3289474
9 0.05207 0.00667 0.3654971
10 0.05588 0.00733 0.4020468
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Sample Calculation:
For liquid - solid fluidized bed
Experimental calculation:
Column diameter, D1 = 2 in. = 0.0508m.
Column area, A1 = 4
D1
2 = 4
(0.0508)2 = 0.0020268m2.
Temperature of water = 230 C.
Density of water, W = 996.787 Kg/m3
Assuming, mf = 0.42
K = H0 (1- mf ) = 0.09779 (1-0.42) m = 0.056718m
For observation no.5 (at decreasing height):
Mass of water, W = 3.25 Kg
Time, t = 30.1 s.
Mass flow rate, .
m = t
W =
1.30
25.3 Kg/s = 0.107973 Kg/s.
Volumetric Flow Rate, V=
.
m
W =
0.1079734
996.787= 10.8321410-5 m3/s
Superficial velocity, u = 1
.
A
V =
10.83214105
0.0020268 m/s = 0.05344m/s.
Height of the bed, H = 0.16002 m.
Voidage, = 1-H
K = 1-
16002.0
0.056718 = 0.64555
From superficial velocity vs. voidage graph for increasing
velocity,
ut = 0.192m/s
umf = 0.01844m/s
n = 2.7007
From superficial velocity vs. voidage graph for decreasing
velocity,
ut = 0.2354m/s
umf = 0.01547m/s
n = 3.1382
Theoretical calculation:
Temperature of water = 260 C.
Density of water, W = 996.787 Kg/m3
-
Viscosity of water, W = 9.3210-4 Kg/ms
g = 9.81 m/s2.
Particle diameter, dp = 1.52410-3m.
Particle density, s = 2.16103 Kg/m3.
Assuming, 0 = 0.42
22
Re''
u
R
W =
2
3
3
)(2
W
WsWp gd
=24
3
)1032.9(3
)787.9962160(81.9787.996001524.02
= 30900.3
Ret = 305. [From 22
Re''
u
R
W vs. Re graph]
Ret = W
Wtpud
ut = Wp
Wt
d
Re =
787.996001524.0
1032.9305 4
= 0.187123 m/s.
umf = 0.0055W
pWs
mf
mf gd
23
)(
1
= 0.00554
23
1032.9
001524.081.9)787.9962160(
42.01
42.0
= 0.01998 m/s.
n = mf
t
mf
u
u
ln
)ln(
= 42.0ln
)187123.0
01998.0ln(
= 2.5787
For gas - solid fluidized bed
Column diameter, D2 = 6 in. = 0.1524 m.
Column area, A2 = 4
D2
2 = 4
0.15242 = 0.01824m2.
For observation no.10
Air flow rate, q = 440 L/min = 100060
440
cm3/s =7.33 310 m3/s.
Superficial velocity of air, u = 2A
q =
01824.0
10 7.33 -3 m/s = 0.40204 m/s.
Pressure drop P = 0.05588 m CCl4
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Graphs:
Figure 4: Variation of Superficial Velocity with voidage
(Increasing flow rate).
y = 0.192x2.7007
0.001
0.01
0.1
1
0.1 1
Sup
erfi
cial
Vel
oci
ty (
m/s
)
Voidage
Variation of Superficial Velocity with voidage (Increasing flow
rate)
0.192
0.42
0.0184
4
-
Figure 5: Variation of Superficial Velocity with voidage
(decreasing flow rate).
y = 0.2354x3.1382
0.001
0.01
0.1
1
0.1 1
Sup
erfi
cial
Vel
oci
ty (m
/s)
Voidage
Variation of Superficial Velocity with voidage (decreasing flow
rate)
0.42
0.01547
0.2354
-
Figure 6: Change of pressure drop with Superficial Air velocity
for 3-D gas-solid
fluidization bed.
0.01
0.1
0.01 0.1 1
Pre
ssu
re D
rop
(m C
Cl 4
)
Superficial Air Velocity(m/s)
Pressure drop vs. Superficial Air velocity for 3-D gas-solid
fluidization bed
-
Results and Discussion:
The result of this experiment has been submitted in a tabular
form as follows
Table 7: Table for results
Topics
Experimental values
for velocity
Theoretical
values Increasing Decreasing
Minimum fluidization
velocity (ms-1)
0.01844 0.01547 0.01998
Terminal settling
velocity (ms-1)
0.192 0.2354 0.123713
Richardson-Zaki index 2.7007 3.1382 2.5787
Pressure drop in gas-solid fluidization ranges from 1.15 inch
CCl4 to 2.20 inch CCl4 for
different air flow rates.
In this experiment two different types of graph have been
plotted which are as follows
Velocity vs voidage in logarithmic coordinates (for increasing
and decreasing velocity)
Pressure drop vs air velocity in logarithmic coordinates
When a fluid is passed upwards through a bed of solids, the
pressure drop across the bed will
be directly proportional to the rate of flow. But when the
frictional drag on the particles
becomes equal to their apparent weight (actual weight less
buoyancy), the particles become
rearranged so that they offer less resistance to the flow of
fluid and the bed starts to expand.
This process continues as the velocity is increased, with the
total frictional force remaining
equal to the weight of the particles, until the bed has assumed
the loosest stable form of packing.
Therefore, the curve between velocity vs voidage in logarithmic
coordinate will be a straight
line and such a curve was also obtained in our experiment. All
the curves plotted are straight
line with positive slopes. This kind of profiles agrees with
literature. As the experiment was
performed for a specific range of fluid velocity, some portion
of the curve was not obtained.
The pressure drop across a bed of solids will be directly
proportional to the rate of flow
when a fluid is passed upwards through it. But when the
frictional drag on the particles becomes
equal to their apparent weight (actual weight less buoyancy),
the particles become rearranged
so that they offer less resistance to the flow of fluid and the
bed starts to expand. This process
continues as the velocity is increased, with the total
frictional force remaining equal to the
weight of the particles, until the bed has assumed the loosest
stable form of packing.
-
Therefore, the curve between velocity vs voidage in logarithmic
coordinate will be a straight
line and such a curve was also obtained in this experiment. All
the curves plotted are straight
line with positive slopes. This kind of profiles agrees with
literature. As the experiment was
performed for a specific range of fluid velocity, the packed bed
region and pneumatic transport
were not observed.
For liquid-solid fluidization the superficial velocity vs.
voidage plot in logarithmic scale
for both the increasing and decreasing height shows straight
line with a slope which was the
Richardson-Zaki index. The Richardson-Zaki indexes found in the
experiment were in the limit
of empirical value 2.7007-3.1382. The pressure drop vs. velocity
graph for gas-solid
fluidization shows like a straight line with positive slope.
This indicates pressure drops
increases linearly with flow rate or velocity.
From results, it is apparent that the experimental values
deviate somewhat from the
theoretical values. Some reasons can be pointed out to explain
these discrepancies.
At higher superficial velocity of the fluid, the bed height was
fluctuating too much. So, it was
very difficult to take the height of the bed and the average
height was taken.
Throughout the calculation, the particles were assumed to be
perfectly spherical. But sand
particles used in the experiment were not spherical.
In this experiment the results were calculated both
theoretically and experimentally.
The discrepancies between the theoretical and experimental
values were not so high. However,
the little difference could be result for the following factors
-
Volumetric flow rate and corresponding bed height were measured
manually. So it
could happen that some mistakes were made which affected the
result of the
experiment.
Again some phenomena like channeling, slugging attrition of
particle occurred due to
which the results varied.
Fluidized beds have a wide range of applications in chemical and
petroleum industries.
One of the main practical advantages of fluidization is
connected with the liquid-like flowing
properties of fluidized beds. Indeed it appears particularly
simple and economical to transport
solid particles through pipes, to control the bed height by
overflow or to circulate from one bed
to another by gravity, thus avoiding the use of standard solid
handling equipment, which is
often mechanically complex and expensive to operate. This
mechanism is used in the
production of vinyl chloride, melamine, poly - ethylene, ploy -
propylene etc. It has its
application in the catalytic cracking of petroleum and also in
filtrate washing. Therefore,
studying this experiment can help to get a conscious
understanding of using the basic principles
of fluidization in process industries.